Pith Number

pith:TVRTNO5I

pith:2012:TVRTNO5IGPFFIQYKCF7I77D5M5

not attested not anchored not stored refs pending

Index Theorems for Polynomial Pencils

Radom\'ir Bos\'ak, Richard Koll\'ar

arxiv:1212.5691 v2 · 2012-12-22 · math.SP · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TVRTNO5IGPFFIQYKCF7I77D5M5}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:22:18.595095Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d6336bba833ca54430a117e8ffc7d674080042d8122ec115c08bbe6f66b8e93

Aliases

arxiv: 1212.5691 · arxiv_version: 1212.5691v2 · doi: 10.48550/arxiv.1212.5691 · pith_short_12: TVRTNO5IGPFF · pith_short_16: TVRTNO5IGPFFIQYK · pith_short_8: TVRTNO5I

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TVRTNO5IGPFFIQYKCF7I77D5M5 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 9d6336bba833ca54430a117e8ffc7d674080042d8122ec115c08bbe6f66b8e93

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c01e0df84756eedecce9758a8a879b75fcaa2db49f6a80917f65dcedd9db24d6",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2012-12-22T13:44:51Z",
    "title_canon_sha256": "4055398be39854ed89737625dd85d11beccb0f812009a021cf6d690fbdd2cd48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.5691",
    "kind": "arxiv",
    "version": 2
  }
}